Question

Vibration

solve with all steps please

(1.2 The following numerical values are given in Problem 1.1: L - 100 in, EI- 108 (lbin?), W = 3000 lb, and k = 2000 lb/in. If the weight W has an ini- tial displacement of yo = 1.0 in and an initial velocity Vo - 20 in/sec, deter- mine the displacement and the velocity 1 sec later.

answer for question 1.1

Answer 1

3 ET 12th a 1 < wn: 1315 + 2K 1 8x to Wn | sx dole + 2x 2000) Hy het -- + 2x gevoy ft x 32,194 4 M 3000 to wna [(*10* + 2x 2000) *12*32: 3000 * Wn= 23.524 nad/ see Yo = 1 in Vo = 20 in/sec Assume, y= Asn (want) at Brookent) 1 @troy:Yo= 1 = 0 +B * B = 1 * = Asm/cont) + 'cos (cat) → Ya Asia (23.524 t) + Coo (23.524 t) + 5 = 2.3. 25+ Aeo[23: 24t) - Sn(23.124+} 20 = 23.584 x A A : 5601A=0.8502 @tzorýzvo= 20 20 23.274

> y = 0,8509 Sin (23-524 +) + cos(23.524+) tin 23.524 40.1509 600 | 23-5248) -Svn (23524t)} #eventh 2000 (23.524+) -23.524 Sin (23.524t) — (ii) Put t= 1 see in cin & 117). y = 0.8601 87 123.524)+600123.524) Al 5= -0.8974 tintes de = 2010 (23-524) - 23.524 60 (23-524) + dy = 22.748 in/see ✓ a